### What time interval should the gyroscope be operated

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A spacecraft is in empty space. It carries on board a gyroscope with a moment of inertia of Ig = 24.0 kg · m2 about the axis of the gyroscope. The moment of inertia of the spacecraft around the same axis is Is = 5.00 105 kg· m2. Neither the spacecraft nor the gyroscope is originally rotating. The gyroscope can be powered up in a negligible period of time to an angular speed of 140 rad/s. If the orientation of the spacecraft is to be changed by 25.0°, for what time interval should the gyroscope be operated? Please explain

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